Properties

Label 32.4.g.a.5.8
Level $32$
Weight $4$
Character 32.5
Analytic conductor $1.888$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [32,4,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.88806112018\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 5.8
Character \(\chi\) \(=\) 32.5
Dual form 32.4.g.a.13.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.49948 - 2.39824i) q^{2} +(2.92731 + 7.06715i) q^{3} +(-3.50313 - 7.19223i) q^{4} +(13.5234 + 5.60159i) q^{5} +(21.3382 + 3.57665i) q^{6} +(-23.0737 - 23.0737i) q^{7} +(-22.5016 - 2.38325i) q^{8} +(-22.2836 + 22.2836i) q^{9} +O(q^{10})\) \(q+(1.49948 - 2.39824i) q^{2} +(2.92731 + 7.06715i) q^{3} +(-3.50313 - 7.19223i) q^{4} +(13.5234 + 5.60159i) q^{5} +(21.3382 + 3.57665i) q^{6} +(-23.0737 - 23.0737i) q^{7} +(-22.5016 - 2.38325i) q^{8} +(-22.2836 + 22.2836i) q^{9} +(33.7121 - 24.0330i) q^{10} +(-7.41078 + 17.8912i) q^{11} +(40.5738 - 45.8110i) q^{12} +(14.8121 - 6.13537i) q^{13} +(-89.9350 + 20.7378i) q^{14} +111.970i q^{15} +(-39.4562 + 50.3905i) q^{16} -27.7996i q^{17} +(20.0277 + 86.8552i) q^{18} +(-82.2959 + 34.0881i) q^{19} +(-7.08639 - 116.887i) q^{20} +(95.5216 - 230.610i) q^{21} +(31.7951 + 44.6003i) q^{22} +(39.2456 - 39.2456i) q^{23} +(-49.0262 - 165.998i) q^{24} +(63.1173 + 63.1173i) q^{25} +(7.49632 - 44.7228i) q^{26} +(-31.8994 - 13.2132i) q^{27} +(-85.1213 + 246.782i) q^{28} +(5.57538 + 13.4602i) q^{29} +(268.531 + 167.896i) q^{30} +155.853 q^{31} +(61.6849 + 170.185i) q^{32} -148.133 q^{33} +(-66.6701 - 41.6849i) q^{34} +(-182.787 - 441.286i) q^{35} +(238.331 + 82.2064i) q^{36} +(188.743 + 78.1798i) q^{37} +(-41.6495 + 248.480i) q^{38} +(86.7192 + 86.7192i) q^{39} +(-290.949 - 158.274i) q^{40} +(113.814 - 113.814i) q^{41} +(-409.825 - 574.878i) q^{42} +(-24.6509 + 59.5126i) q^{43} +(154.638 - 9.37513i) q^{44} +(-426.174 + 176.527i) q^{45} +(-35.2725 - 152.968i) q^{46} +217.464i q^{47} +(-471.618 - 131.334i) q^{48} +721.795i q^{49} +(246.014 - 56.7275i) q^{50} +(196.464 - 81.3779i) q^{51} +(-96.0156 - 85.0390i) q^{52} +(-35.7808 + 86.3826i) q^{53} +(-79.5208 + 56.6896i) q^{54} +(-200.438 + 200.438i) q^{55} +(464.205 + 574.186i) q^{56} +(-481.811 - 481.811i) q^{57} +(40.6409 + 6.81211i) q^{58} +(-116.586 - 48.2914i) q^{59} +(805.312 - 392.244i) q^{60} +(-197.015 - 475.636i) q^{61} +(233.699 - 373.774i) q^{62} +1028.33 q^{63} +(500.640 + 107.254i) q^{64} +234.678 q^{65} +(-222.123 + 355.260i) q^{66} +(144.765 + 349.494i) q^{67} +(-199.941 + 97.3854i) q^{68} +(392.239 + 162.471i) q^{69} +(-1332.40 - 223.333i) q^{70} +(-523.475 - 523.475i) q^{71} +(554.523 - 448.308i) q^{72} +(-718.521 + 718.521i) q^{73} +(470.510 - 335.422i) q^{74} +(-261.296 + 630.823i) q^{75} +(533.462 + 472.476i) q^{76} +(583.811 - 241.822i) q^{77} +(338.007 - 77.9399i) q^{78} -958.779i q^{79} +(-815.851 + 460.436i) q^{80} +586.755i q^{81} +(-102.292 - 443.614i) q^{82} +(1241.90 - 514.414i) q^{83} +(-1993.22 + 120.841i) q^{84} +(155.722 - 375.946i) q^{85} +(105.762 + 148.357i) q^{86} +(-78.8041 + 78.8041i) q^{87} +(209.393 - 384.918i) q^{88} +(-808.016 - 808.016i) q^{89} +(-215.685 + 1286.77i) q^{90} +(-483.336 - 200.204i) q^{91} +(-419.746 - 144.781i) q^{92} +(456.231 + 1101.44i) q^{93} +(521.531 + 326.083i) q^{94} -1303.87 q^{95} +(-1022.15 + 934.121i) q^{96} +1399.29 q^{97} +(1731.04 + 1082.32i) q^{98} +(-233.541 - 563.819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.49948 2.39824i 0.530146 0.847906i
\(3\) 2.92731 + 7.06715i 0.563361 + 1.36007i 0.907063 + 0.420995i \(0.138319\pi\)
−0.343702 + 0.939079i \(0.611681\pi\)
\(4\) −3.50313 7.19223i −0.437891 0.899028i
\(5\) 13.5234 + 5.60159i 1.20957 + 0.501022i 0.894081 0.447906i \(-0.147830\pi\)
0.315493 + 0.948928i \(0.397830\pi\)
\(6\) 21.3382 + 3.57665i 1.45188 + 0.243360i
\(7\) −23.0737 23.0737i −1.24586 1.24586i −0.957530 0.288335i \(-0.906898\pi\)
−0.288335 0.957530i \(-0.593102\pi\)
\(8\) −22.5016 2.38325i −0.994438 0.105326i
\(9\) −22.2836 + 22.2836i −0.825318 + 0.825318i
\(10\) 33.7121 24.0330i 1.06607 0.759990i
\(11\) −7.41078 + 17.8912i −0.203130 + 0.490400i −0.992312 0.123760i \(-0.960505\pi\)
0.789182 + 0.614159i \(0.210505\pi\)
\(12\) 40.5738 45.8110i 0.976054 1.10204i
\(13\) 14.8121 6.13537i 0.316010 0.130896i −0.219040 0.975716i \(-0.570293\pi\)
0.535051 + 0.844820i \(0.320293\pi\)
\(14\) −89.9350 + 20.7378i −1.71687 + 0.395887i
\(15\) 111.970i 1.92737i
\(16\) −39.4562 + 50.3905i −0.616504 + 0.787352i
\(17\) 27.7996i 0.396611i −0.980140 0.198305i \(-0.936456\pi\)
0.980140 0.198305i \(-0.0635438\pi\)
\(18\) 20.0277 + 86.8552i 0.262254 + 1.13733i
\(19\) −82.2959 + 34.0881i −0.993683 + 0.411597i −0.819477 0.573112i \(-0.805736\pi\)
−0.174206 + 0.984709i \(0.555736\pi\)
\(20\) −7.08639 116.887i −0.0792283 1.30683i
\(21\) 95.5216 230.610i 0.992596 2.39634i
\(22\) 31.7951 + 44.6003i 0.308125 + 0.432219i
\(23\) 39.2456 39.2456i 0.355795 0.355795i −0.506466 0.862260i \(-0.669048\pi\)
0.862260 + 0.506466i \(0.169048\pi\)
\(24\) −49.0262 165.998i −0.416977 1.41185i
\(25\) 63.1173 + 63.1173i 0.504938 + 0.504938i
\(26\) 7.49632 44.7228i 0.0565442 0.337341i
\(27\) −31.8994 13.2132i −0.227372 0.0941805i
\(28\) −85.1213 + 246.782i −0.574515 + 1.66562i
\(29\) 5.57538 + 13.4602i 0.0357008 + 0.0861892i 0.940724 0.339172i \(-0.110147\pi\)
−0.905024 + 0.425362i \(0.860147\pi\)
\(30\) 268.531 + 167.896i 1.63423 + 1.02178i
\(31\) 155.853 0.902970 0.451485 0.892279i \(-0.350894\pi\)
0.451485 + 0.892279i \(0.350894\pi\)
\(32\) 61.6849 + 170.185i 0.340764 + 0.940149i
\(33\) −148.133 −0.781416
\(34\) −66.6701 41.6849i −0.336289 0.210262i
\(35\) −182.787 441.286i −0.882760 2.13117i
\(36\) 238.331 + 82.2064i 1.10338 + 0.380585i
\(37\) 188.743 + 78.1798i 0.838625 + 0.347370i 0.760311 0.649559i \(-0.225046\pi\)
0.0783139 + 0.996929i \(0.475046\pi\)
\(38\) −41.6495 + 248.480i −0.177801 + 1.06076i
\(39\) 86.7192 + 86.7192i 0.356056 + 0.356056i
\(40\) −290.949 158.274i −1.15007 0.625634i
\(41\) 113.814 113.814i 0.433530 0.433530i −0.456297 0.889827i \(-0.650825\pi\)
0.889827 + 0.456297i \(0.150825\pi\)
\(42\) −409.825 574.878i −1.50565 2.11204i
\(43\) −24.6509 + 59.5126i −0.0874240 + 0.211060i −0.961545 0.274649i \(-0.911438\pi\)
0.874121 + 0.485709i \(0.161438\pi\)
\(44\) 154.638 9.37513i 0.529832 0.0321217i
\(45\) −426.174 + 176.527i −1.41179 + 0.584781i
\(46\) −35.2725 152.968i −0.113058 0.490304i
\(47\) 217.464i 0.674902i 0.941343 + 0.337451i \(0.109565\pi\)
−0.941343 + 0.337451i \(0.890435\pi\)
\(48\) −471.618 131.334i −1.41817 0.394927i
\(49\) 721.795i 2.10436i
\(50\) 246.014 56.7275i 0.695831 0.160449i
\(51\) 196.464 81.3779i 0.539420 0.223435i
\(52\) −96.0156 85.0390i −0.256057 0.226784i
\(53\) −35.7808 + 86.3826i −0.0927335 + 0.223879i −0.963440 0.267925i \(-0.913662\pi\)
0.870706 + 0.491803i \(0.163662\pi\)
\(54\) −79.5208 + 56.6896i −0.200397 + 0.142861i
\(55\) −200.438 + 200.438i −0.491402 + 0.491402i
\(56\) 464.205 + 574.186i 1.10771 + 1.37016i
\(57\) −481.811 481.811i −1.11960 1.11960i
\(58\) 40.6409 + 6.81211i 0.0920070 + 0.0154220i
\(59\) −116.586 48.2914i −0.257257 0.106559i 0.250328 0.968161i \(-0.419462\pi\)
−0.507585 + 0.861602i \(0.669462\pi\)
\(60\) 805.312 392.244i 1.73276 0.843975i
\(61\) −197.015 475.636i −0.413528 0.998344i −0.984183 0.177155i \(-0.943311\pi\)
0.570655 0.821190i \(-0.306689\pi\)
\(62\) 233.699 373.774i 0.478706 0.765634i
\(63\) 1028.33 2.05647
\(64\) 500.640 + 107.254i 0.977813 + 0.209480i
\(65\) 234.678 0.447819
\(66\) −222.123 + 355.260i −0.414264 + 0.662567i
\(67\) 144.765 + 349.494i 0.263968 + 0.637276i 0.999177 0.0405648i \(-0.0129157\pi\)
−0.735208 + 0.677841i \(0.762916\pi\)
\(68\) −199.941 + 97.3854i −0.356564 + 0.173672i
\(69\) 392.239 + 162.471i 0.684348 + 0.283466i
\(70\) −1332.40 223.333i −2.27502 0.381334i
\(71\) −523.475 523.475i −0.875001 0.875001i 0.118011 0.993012i \(-0.462348\pi\)
−0.993012 + 0.118011i \(0.962348\pi\)
\(72\) 554.523 448.308i 0.907655 0.733800i
\(73\) −718.521 + 718.521i −1.15201 + 1.15201i −0.165856 + 0.986150i \(0.553039\pi\)
−0.986150 + 0.165856i \(0.946961\pi\)
\(74\) 470.510 335.422i 0.739131 0.526919i
\(75\) −261.296 + 630.823i −0.402291 + 0.971216i
\(76\) 533.462 + 472.476i 0.805162 + 0.713115i
\(77\) 583.811 241.822i 0.864045 0.357899i
\(78\) 338.007 77.9399i 0.490664 0.113141i
\(79\) 958.779i 1.36546i −0.730673 0.682728i \(-0.760793\pi\)
0.730673 0.682728i \(-0.239207\pi\)
\(80\) −815.851 + 460.436i −1.14019 + 0.643479i
\(81\) 586.755i 0.804876i
\(82\) −102.292 443.614i −0.137759 0.597427i
\(83\) 1241.90 514.414i 1.64237 0.680292i 0.645836 0.763476i \(-0.276509\pi\)
0.996534 + 0.0831842i \(0.0265090\pi\)
\(84\) −1993.22 + 120.841i −2.58903 + 0.156963i
\(85\) 155.722 375.946i 0.198711 0.479730i
\(86\) 105.762 + 148.357i 0.132612 + 0.186020i
\(87\) −78.8041 + 78.8041i −0.0971113 + 0.0971113i
\(88\) 209.393 384.918i 0.253652 0.466277i
\(89\) −808.016 808.016i −0.962354 0.962354i 0.0369622 0.999317i \(-0.488232\pi\)
−0.999317 + 0.0369622i \(0.988232\pi\)
\(90\) −215.685 + 1286.77i −0.252613 + 1.50708i
\(91\) −483.336 200.204i −0.556785 0.230628i
\(92\) −419.746 144.781i −0.475669 0.164070i
\(93\) 456.231 + 1101.44i 0.508698 + 1.22811i
\(94\) 521.531 + 326.083i 0.572253 + 0.357796i
\(95\) −1303.87 −1.40815
\(96\) −1022.15 + 934.121i −1.08670 + 0.993108i
\(97\) 1399.29 1.46471 0.732354 0.680924i \(-0.238422\pi\)
0.732354 + 0.680924i \(0.238422\pi\)
\(98\) 1731.04 + 1082.32i 1.78430 + 1.11562i
\(99\) −233.541 563.819i −0.237089 0.572383i
\(100\) 232.846 675.062i 0.232846 0.675062i
\(101\) −1024.11 424.200i −1.00894 0.417916i −0.183871 0.982950i \(-0.558863\pi\)
−0.825067 + 0.565035i \(0.808863\pi\)
\(102\) 99.4293 593.192i 0.0965193 0.575831i
\(103\) −483.862 483.862i −0.462877 0.462877i 0.436720 0.899597i \(-0.356140\pi\)
−0.899597 + 0.436720i \(0.856140\pi\)
\(104\) −347.917 + 102.754i −0.328039 + 0.0968837i
\(105\) 2583.56 2583.56i 2.40124 2.40124i
\(106\) 153.514 + 215.340i 0.140666 + 0.197318i
\(107\) −682.420 + 1647.51i −0.616561 + 1.48851i 0.239112 + 0.970992i \(0.423144\pi\)
−0.855673 + 0.517517i \(0.826856\pi\)
\(108\) 16.7155 + 275.715i 0.0148931 + 0.245655i
\(109\) −1813.85 + 751.322i −1.59390 + 0.660217i −0.990537 0.137247i \(-0.956175\pi\)
−0.603367 + 0.797463i \(0.706175\pi\)
\(110\) 180.147 + 781.253i 0.156148 + 0.677178i
\(111\) 1562.73i 1.33629i
\(112\) 2073.10 252.295i 1.74901 0.212854i
\(113\) 1392.34i 1.15912i −0.814931 0.579558i \(-0.803225\pi\)
0.814931 0.579558i \(-0.196775\pi\)
\(114\) −1877.97 + 433.034i −1.54287 + 0.355766i
\(115\) 750.574 310.898i 0.608621 0.252099i
\(116\) 77.2772 87.2520i 0.0618535 0.0698374i
\(117\) −193.349 + 466.785i −0.152778 + 0.368840i
\(118\) −290.632 + 207.189i −0.226736 + 0.161638i
\(119\) −641.440 + 641.440i −0.494123 + 0.494123i
\(120\) 266.852 2519.49i 0.203001 1.91664i
\(121\) 675.984 + 675.984i 0.507877 + 0.507877i
\(122\) −1436.11 240.717i −1.06573 0.178635i
\(123\) 1137.51 + 471.171i 0.833867 + 0.345399i
\(124\) −545.974 1120.93i −0.395402 0.811796i
\(125\) −200.193 483.310i −0.143247 0.345828i
\(126\) 1541.96 2466.19i 1.09023 1.74369i
\(127\) 909.845 0.635714 0.317857 0.948139i \(-0.397037\pi\)
0.317857 + 0.948139i \(0.397037\pi\)
\(128\) 1007.92 1039.83i 0.696003 0.718039i
\(129\) −492.746 −0.336309
\(130\) 351.895 562.815i 0.237410 0.379709i
\(131\) 375.465 + 906.452i 0.250416 + 0.604558i 0.998238 0.0593418i \(-0.0189002\pi\)
−0.747822 + 0.663900i \(0.768900\pi\)
\(132\) 518.930 + 1065.41i 0.342175 + 0.702515i
\(133\) 2685.41 + 1112.34i 1.75079 + 0.725201i
\(134\) 1055.24 + 176.877i 0.680292 + 0.114029i
\(135\) −357.375 357.375i −0.227837 0.227837i
\(136\) −66.2533 + 625.534i −0.0417734 + 0.394405i
\(137\) −821.434 + 821.434i −0.512262 + 0.512262i −0.915219 0.402957i \(-0.867982\pi\)
0.402957 + 0.915219i \(0.367982\pi\)
\(138\) 977.798 697.062i 0.603157 0.429985i
\(139\) 673.401 1625.73i 0.410915 0.992036i −0.573978 0.818871i \(-0.694600\pi\)
0.984893 0.173165i \(-0.0553995\pi\)
\(140\) −2533.50 + 2860.52i −1.52943 + 1.72685i
\(141\) −1536.85 + 636.584i −0.917916 + 0.380213i
\(142\) −2040.36 + 470.480i −1.20580 + 0.278041i
\(143\) 310.474i 0.181560i
\(144\) −243.656 2002.11i −0.141004 1.15863i
\(145\) 213.259i 0.122139i
\(146\) 645.779 + 2800.59i 0.366062 + 1.58753i
\(147\) −5101.03 + 2112.92i −2.86208 + 1.18551i
\(148\) −98.9027 1631.36i −0.0549308 0.906058i
\(149\) 247.105 596.564i 0.135863 0.328003i −0.841275 0.540607i \(-0.818195\pi\)
0.977138 + 0.212604i \(0.0681946\pi\)
\(150\) 1121.06 + 1572.56i 0.610227 + 0.855991i
\(151\) 373.703 373.703i 0.201401 0.201401i −0.599199 0.800600i \(-0.704514\pi\)
0.800600 + 0.599199i \(0.204514\pi\)
\(152\) 1933.03 570.903i 1.03151 0.304647i
\(153\) 619.474 + 619.474i 0.327330 + 0.327330i
\(154\) 295.464 1762.73i 0.154605 0.922368i
\(155\) 2107.67 + 873.027i 1.09221 + 0.452408i
\(156\) 319.916 927.492i 0.164191 0.476018i
\(157\) −186.690 450.709i −0.0949011 0.229112i 0.869299 0.494286i \(-0.164570\pi\)
−0.964200 + 0.265174i \(0.914570\pi\)
\(158\) −2299.38 1437.67i −1.15778 0.723891i
\(159\) −715.220 −0.356734
\(160\) −119.116 + 2647.02i −0.0588557 + 1.30791i
\(161\) −1811.09 −0.886544
\(162\) 1407.18 + 879.826i 0.682460 + 0.426702i
\(163\) −495.962 1197.36i −0.238324 0.575364i 0.758786 0.651340i \(-0.225793\pi\)
−0.997110 + 0.0759758i \(0.975793\pi\)
\(164\) −1217.28 419.871i −0.579595 0.199917i
\(165\) −2003.27 829.783i −0.945180 0.391506i
\(166\) 628.521 3749.74i 0.293872 1.75323i
\(167\) −644.684 644.684i −0.298725 0.298725i 0.541789 0.840514i \(-0.317747\pi\)
−0.840514 + 0.541789i \(0.817747\pi\)
\(168\) −2698.99 + 4961.42i −1.23947 + 2.27846i
\(169\) −1371.76 + 1371.76i −0.624378 + 0.624378i
\(170\) −668.107 937.181i −0.301420 0.422815i
\(171\) 1074.24 2593.45i 0.480406 1.15980i
\(172\) 514.384 31.1851i 0.228031 0.0138247i
\(173\) 2383.01 987.076i 1.04727 0.433792i 0.208351 0.978054i \(-0.433190\pi\)
0.838915 + 0.544262i \(0.183190\pi\)
\(174\) 70.8262 + 307.156i 0.0308581 + 0.133824i
\(175\) 2912.70i 1.25817i
\(176\) −609.146 1079.35i −0.260887 0.462268i
\(177\) 965.293i 0.409920i
\(178\) −3149.42 + 726.215i −1.32617 + 0.305798i
\(179\) 3184.86 1319.21i 1.32987 0.550852i 0.399254 0.916840i \(-0.369269\pi\)
0.930619 + 0.365988i \(0.119269\pi\)
\(180\) 2762.57 + 2446.75i 1.14394 + 1.01316i
\(181\) −820.433 + 1980.70i −0.336919 + 0.813394i 0.661089 + 0.750307i \(0.270094\pi\)
−0.998008 + 0.0630866i \(0.979906\pi\)
\(182\) −1204.89 + 858.955i −0.490728 + 0.349835i
\(183\) 2784.67 2784.67i 1.12486 1.12486i
\(184\) −976.620 + 789.556i −0.391290 + 0.316341i
\(185\) 2114.52 + 2114.52i 0.840339 + 0.840339i
\(186\) 3325.62 + 557.432i 1.31100 + 0.219747i
\(187\) 497.368 + 206.016i 0.194498 + 0.0805637i
\(188\) 1564.05 761.803i 0.606756 0.295533i
\(189\) 431.161 + 1040.92i 0.165938 + 0.400611i
\(190\) −1955.13 + 3127.00i −0.746526 + 1.19398i
\(191\) −330.108 −0.125056 −0.0625282 0.998043i \(-0.519916\pi\)
−0.0625282 + 0.998043i \(0.519916\pi\)
\(192\) 707.551 + 3852.06i 0.265954 + 1.44791i
\(193\) −914.905 −0.341224 −0.170612 0.985338i \(-0.554575\pi\)
−0.170612 + 0.985338i \(0.554575\pi\)
\(194\) 2098.21 3355.84i 0.776509 1.24194i
\(195\) 686.976 + 1658.51i 0.252284 + 0.609068i
\(196\) 5191.31 2528.54i 1.89188 0.921479i
\(197\) −41.3093 17.1109i −0.0149399 0.00618832i 0.375201 0.926943i \(-0.377574\pi\)
−0.390141 + 0.920755i \(0.627574\pi\)
\(198\) −1702.36 285.346i −0.611019 0.102417i
\(199\) 2946.98 + 2946.98i 1.04978 + 1.04978i 0.998694 + 0.0510831i \(0.0162673\pi\)
0.0510831 + 0.998694i \(0.483733\pi\)
\(200\) −1269.81 1570.66i −0.448947 0.555313i
\(201\) −2046.16 + 2046.16i −0.718033 + 0.718033i
\(202\) −2552.97 + 1819.98i −0.889238 + 0.633929i
\(203\) 181.931 439.221i 0.0629018 0.151858i
\(204\) −1273.53 1127.93i −0.437081 0.387114i
\(205\) 2176.69 901.616i 0.741594 0.307178i
\(206\) −1885.96 + 434.877i −0.637869 + 0.147084i
\(207\) 1749.07i 0.587288i
\(208\) −275.265 + 988.468i −0.0917605 + 0.329509i
\(209\) 1724.99i 0.570910i
\(210\) −2322.01 10070.0i −0.763018 3.30903i
\(211\) 1661.58 688.250i 0.542124 0.224555i −0.0947802 0.995498i \(-0.530215\pi\)
0.636904 + 0.770943i \(0.280215\pi\)
\(212\) 746.628 45.2652i 0.241880 0.0146643i
\(213\) 2167.10 5231.85i 0.697124 1.68301i
\(214\) 2927.84 + 4107.01i 0.935249 + 1.31191i
\(215\) −666.731 + 666.731i −0.211492 + 0.211492i
\(216\) 686.296 + 373.341i 0.216188 + 0.117605i
\(217\) −3596.12 3596.12i −1.12498 1.12498i
\(218\) −917.981 + 5476.65i −0.285200 + 1.70149i
\(219\) −7181.22 2974.56i −2.21581 0.917818i
\(220\) 2143.76 + 739.438i 0.656965 + 0.226604i
\(221\) −170.561 411.770i −0.0519147 0.125333i
\(222\) 3747.81 + 2343.28i 1.13305 + 0.708427i
\(223\) −2657.54 −0.798035 −0.399018 0.916943i \(-0.630649\pi\)
−0.399018 + 0.916943i \(0.630649\pi\)
\(224\) 2503.51 5350.11i 0.746752 1.59584i
\(225\) −2812.96 −0.833470
\(226\) −3339.16 2087.78i −0.982821 0.614500i
\(227\) 833.769 + 2012.90i 0.243785 + 0.588549i 0.997653 0.0684772i \(-0.0218140\pi\)
−0.753868 + 0.657026i \(0.771814\pi\)
\(228\) −1777.45 + 5153.14i −0.516292 + 1.49682i
\(229\) −5607.23 2322.59i −1.61806 0.670224i −0.624244 0.781230i \(-0.714593\pi\)
−0.993820 + 0.111006i \(0.964593\pi\)
\(230\) 379.862 2266.24i 0.108901 0.649703i
\(231\) 3417.99 + 3417.99i 0.973538 + 0.973538i
\(232\) −93.3758 316.162i −0.0264242 0.0894700i
\(233\) 132.710 132.710i 0.0373138 0.0373138i −0.688204 0.725518i \(-0.741600\pi\)
0.725518 + 0.688204i \(0.241600\pi\)
\(234\) 829.540 + 1163.63i 0.231747 + 0.325081i
\(235\) −1218.14 + 2940.86i −0.338140 + 0.816343i
\(236\) 61.0919 + 1007.68i 0.0168506 + 0.277943i
\(237\) 6775.83 2806.64i 1.85712 0.769245i
\(238\) 576.502 + 2500.15i 0.157013 + 0.680928i
\(239\) 138.825i 0.0375727i 0.999824 + 0.0187863i \(0.00598023\pi\)
−0.999824 + 0.0187863i \(0.994020\pi\)
\(240\) −5642.22 4417.91i −1.51752 1.18823i
\(241\) 4825.11i 1.28968i 0.764318 + 0.644839i \(0.223076\pi\)
−0.764318 + 0.644839i \(0.776924\pi\)
\(242\) 2634.80 607.549i 0.699881 0.161383i
\(243\) −5007.97 + 2074.37i −1.32206 + 0.547616i
\(244\) −2730.72 + 3083.19i −0.716460 + 0.808939i
\(245\) −4043.20 + 9761.15i −1.05433 + 2.54537i
\(246\) 2835.65 2021.51i 0.734937 0.523929i
\(247\) −1009.83 + 1009.83i −0.260138 + 0.260138i
\(248\) −3506.94 371.437i −0.897948 0.0951061i
\(249\) 7270.88 + 7270.88i 1.85049 + 1.85049i
\(250\) −1459.28 244.601i −0.369172 0.0618796i
\(251\) −3296.58 1365.49i −0.828996 0.343381i −0.0724909 0.997369i \(-0.523095\pi\)
−0.756505 + 0.653988i \(0.773095\pi\)
\(252\) −3602.37 7395.99i −0.900509 1.84882i
\(253\) 411.311 + 992.992i 0.102209 + 0.246754i
\(254\) 1364.29 2182.03i 0.337021 0.539026i
\(255\) 3112.71 0.764414
\(256\) −982.413 3976.44i −0.239847 0.970811i
\(257\) 6601.51 1.60230 0.801149 0.598465i \(-0.204222\pi\)
0.801149 + 0.598465i \(0.204222\pi\)
\(258\) −738.862 + 1181.72i −0.178293 + 0.285158i
\(259\) −2551.10 6158.90i −0.612038 1.47759i
\(260\) −822.108 1687.86i −0.196096 0.402602i
\(261\) −424.180 175.701i −0.100598 0.0416691i
\(262\) 2736.89 + 458.751i 0.645366 + 0.108174i
\(263\) 4812.19 + 4812.19i 1.12826 + 1.12826i 0.990460 + 0.137799i \(0.0440028\pi\)
0.137799 + 0.990460i \(0.455997\pi\)
\(264\) 3333.23 + 353.039i 0.777069 + 0.0823032i
\(265\) −967.760 + 967.760i −0.224336 + 0.224336i
\(266\) 6694.37 4772.35i 1.54308 1.10004i
\(267\) 3345.06 8075.69i 0.766720 1.85103i
\(268\) 2006.51 2265.51i 0.457340 0.516372i
\(269\) 952.102 394.374i 0.215802 0.0893880i −0.272164 0.962251i \(-0.587739\pi\)
0.487965 + 0.872863i \(0.337739\pi\)
\(270\) −1392.95 + 321.195i −0.313971 + 0.0723975i
\(271\) 134.675i 0.0301880i −0.999886 0.0150940i \(-0.995195\pi\)
0.999886 0.0150940i \(-0.00480475\pi\)
\(272\) 1400.83 + 1096.87i 0.312272 + 0.244512i
\(273\) 4001.87i 0.887195i
\(274\) 738.274 + 3201.72i 0.162776 + 0.705923i
\(275\) −1596.99 + 661.496i −0.350190 + 0.145053i
\(276\) −205.536 3390.23i −0.0448255 0.739375i
\(277\) 196.577 474.579i 0.0426396 0.102941i −0.901125 0.433560i \(-0.857257\pi\)
0.943764 + 0.330619i \(0.107257\pi\)
\(278\) −2889.15 4052.73i −0.623309 0.874341i
\(279\) −3472.97 + 3472.97i −0.745238 + 0.745238i
\(280\) 3061.29 + 10365.2i 0.653382 + 2.21229i
\(281\) −5752.69 5752.69i −1.22127 1.22127i −0.967181 0.254087i \(-0.918225\pi\)
−0.254087 0.967181i \(-0.581775\pi\)
\(282\) −777.792 + 4640.28i −0.164244 + 0.979875i
\(283\) −30.6153 12.6813i −0.00643071 0.00266369i 0.379466 0.925206i \(-0.376108\pi\)
−0.385896 + 0.922542i \(0.626108\pi\)
\(284\) −1931.15 + 5598.75i −0.403496 + 1.16981i
\(285\) −3816.84 9214.66i −0.793298 1.91519i
\(286\) 744.592 + 465.549i 0.153946 + 0.0962535i
\(287\) −5252.22 −1.08024
\(288\) −5166.90 2417.77i −1.05716 0.494683i
\(289\) 4140.18 0.842700
\(290\) 511.446 + 319.777i 0.103563 + 0.0647515i
\(291\) 4096.16 + 9889.01i 0.825159 + 1.99211i
\(292\) 7684.83 + 2650.69i 1.54014 + 0.531233i
\(293\) 6083.38 + 2519.82i 1.21295 + 0.502421i 0.895163 0.445740i \(-0.147059\pi\)
0.317790 + 0.948161i \(0.397059\pi\)
\(294\) −2581.61 + 15401.8i −0.512117 + 3.05527i
\(295\) −1306.13 1306.13i −0.257783 0.257783i
\(296\) −4060.69 2208.99i −0.797374 0.433767i
\(297\) 472.799 472.799i 0.0923722 0.0923722i
\(298\) −1060.18 1487.15i −0.206088 0.289088i
\(299\) 340.523 822.096i 0.0658628 0.159007i
\(300\) 5452.37 330.556i 1.04931 0.0636156i
\(301\) 1941.97 804.390i 0.371871 0.154034i
\(302\) −335.870 1456.59i −0.0639972 0.277541i
\(303\) 8479.30i 1.60767i
\(304\) 1529.37 5491.92i 0.288537 1.03613i
\(305\) 7535.84i 1.41476i
\(306\) 2414.54 556.760i 0.451078 0.104013i
\(307\) −5493.47 + 2275.47i −1.02127 + 0.423022i −0.829553 0.558428i \(-0.811405\pi\)
−0.191714 + 0.981451i \(0.561405\pi\)
\(308\) −3784.41 3351.77i −0.700119 0.620080i
\(309\) 2003.11 4835.94i 0.368780 0.890314i
\(310\) 5254.14 3745.62i 0.962629 0.686249i
\(311\) −640.062 + 640.062i −0.116703 + 0.116703i −0.763047 0.646344i \(-0.776297\pi\)
0.646344 + 0.763047i \(0.276297\pi\)
\(312\) −1744.64 2157.99i −0.316574 0.391577i
\(313\) 571.963 + 571.963i 0.103288 + 0.103288i 0.756862 0.653574i \(-0.226731\pi\)
−0.653574 + 0.756862i \(0.726731\pi\)
\(314\) −1360.85 228.102i −0.244577 0.0409953i
\(315\) 13906.6 + 5760.29i 2.48745 + 1.03034i
\(316\) −6895.75 + 3358.72i −1.22758 + 0.597920i
\(317\) 1686.24 + 4070.95i 0.298766 + 0.721284i 0.999965 + 0.00831921i \(0.00264812\pi\)
−0.701200 + 0.712965i \(0.747352\pi\)
\(318\) −1072.46 + 1715.27i −0.189121 + 0.302477i
\(319\) −282.136 −0.0495191
\(320\) 6169.59 + 4254.82i 1.07778 + 0.743287i
\(321\) −13640.8 −2.37183
\(322\) −2715.69 + 4343.42i −0.469998 + 0.751706i
\(323\) 947.634 + 2287.79i 0.163244 + 0.394106i
\(324\) 4220.07 2055.47i 0.723606 0.352448i
\(325\) 1322.15 + 547.651i 0.225660 + 0.0934715i
\(326\) −3615.24 605.977i −0.614201 0.102951i
\(327\) −10619.4 10619.4i −1.79589 1.79589i
\(328\) −2832.24 + 2289.74i −0.476781 + 0.385457i
\(329\) 5017.70 5017.70i 0.840836 0.840836i
\(330\) −4993.89 + 3560.09i −0.833044 + 0.593869i
\(331\) −2604.99 + 6288.99i −0.432577 + 1.04433i 0.545877 + 0.837866i \(0.316197\pi\)
−0.978453 + 0.206467i \(0.933803\pi\)
\(332\) −8050.33 7130.00i −1.33078 1.17864i
\(333\) −5948.00 + 2463.74i −0.978823 + 0.405442i
\(334\) −2512.80 + 579.418i −0.411659 + 0.0949232i
\(335\) 5537.28i 0.903086i
\(336\) 7851.62 + 13912.4i 1.27482 + 2.25887i
\(337\) 5051.39i 0.816518i 0.912866 + 0.408259i \(0.133864\pi\)
−0.912866 + 0.408259i \(0.866136\pi\)
\(338\) 1232.88 + 5346.73i 0.198403 + 0.860425i
\(339\) 9839.85 4075.80i 1.57648 0.653000i
\(340\) −3249.40 + 196.999i −0.518304 + 0.0314228i
\(341\) −1154.99 + 2788.40i −0.183421 + 0.442817i
\(342\) −4608.92 6465.13i −0.728719 1.02220i
\(343\) 8740.21 8740.21i 1.37588 1.37588i
\(344\) 696.518 1280.38i 0.109168 0.200678i
\(345\) 4394.32 + 4394.32i 0.685746 + 0.685746i
\(346\) 1206.03 7195.14i 0.187389 1.11796i
\(347\) 1548.08 + 641.238i 0.239497 + 0.0992030i 0.499204 0.866485i \(-0.333626\pi\)
−0.259707 + 0.965688i \(0.583626\pi\)
\(348\) 842.837 + 290.716i 0.129830 + 0.0447817i
\(349\) 3012.90 + 7273.78i 0.462111 + 1.11563i 0.967529 + 0.252760i \(0.0813383\pi\)
−0.505418 + 0.862875i \(0.668662\pi\)
\(350\) −6985.37 4367.54i −1.06681 0.667013i
\(351\) −553.564 −0.0841797
\(352\) −3501.95 157.587i −0.530268 0.0238620i
\(353\) −3877.72 −0.584675 −0.292337 0.956315i \(-0.594433\pi\)
−0.292337 + 0.956315i \(0.594433\pi\)
\(354\) −2315.01 1447.44i −0.347574 0.217317i
\(355\) −4146.89 10011.5i −0.619983 1.49677i
\(356\) −2980.85 + 8642.02i −0.443778 + 1.28659i
\(357\) −6410.84 2655.46i −0.950414 0.393674i
\(358\) 1611.84 9616.19i 0.237956 1.41964i
\(359\) −80.3532 80.3532i −0.0118130 0.0118130i 0.701176 0.712989i \(-0.252659\pi\)
−0.712989 + 0.701176i \(0.752659\pi\)
\(360\) 10010.3 2956.46i 1.46553 0.432831i
\(361\) 760.577 760.577i 0.110887 0.110887i
\(362\) 3519.98 + 4937.61i 0.511066 + 0.716893i
\(363\) −2798.47 + 6756.09i −0.404632 + 0.976867i
\(364\) 253.272 + 4177.61i 0.0364700 + 0.601555i
\(365\) −13741.7 + 5692.01i −1.97062 + 0.816256i
\(366\) −2502.76 10853.9i −0.357435 1.55011i
\(367\) 2569.61i 0.365484i −0.983161 0.182742i \(-0.941503\pi\)
0.983161 0.182742i \(-0.0584973\pi\)
\(368\) 429.124 + 3526.09i 0.0607870 + 0.499484i
\(369\) 5072.36i 0.715601i
\(370\) 8241.81 1900.45i 1.15803 0.267027i
\(371\) 2818.77 1167.57i 0.394456 0.163389i
\(372\) 6323.56 7139.79i 0.881348 0.995110i
\(373\) 3461.88 8357.71i 0.480561 1.16018i −0.478782 0.877934i \(-0.658922\pi\)
0.959343 0.282243i \(-0.0910785\pi\)
\(374\) 1239.87 883.890i 0.171423 0.122206i
\(375\) 2829.60 2829.60i 0.389652 0.389652i
\(376\) 518.271 4893.28i 0.0710845 0.671148i
\(377\) 165.166 + 165.166i 0.0225636 + 0.0225636i
\(378\) 3142.88 + 526.802i 0.427652 + 0.0716819i
\(379\) 200.232 + 82.9388i 0.0271378 + 0.0112408i 0.396211 0.918159i \(-0.370325\pi\)
−0.369073 + 0.929400i \(0.620325\pi\)
\(380\) 4567.63 + 9377.74i 0.616617 + 1.26597i
\(381\) 2663.40 + 6430.01i 0.358136 + 0.864618i
\(382\) −494.990 + 791.679i −0.0662982 + 0.106036i
\(383\) −4511.40 −0.601885 −0.300942 0.953642i \(-0.597301\pi\)
−0.300942 + 0.953642i \(0.597301\pi\)
\(384\) 10299.1 + 4079.21i 1.36869 + 0.542100i
\(385\) 9249.73 1.22444
\(386\) −1371.88 + 2194.16i −0.180899 + 0.289326i
\(387\) −776.844 1875.47i −0.102039 0.246345i
\(388\) −4901.90 10064.0i −0.641382 1.31681i
\(389\) 4993.23 + 2068.26i 0.650814 + 0.269576i 0.683567 0.729887i \(-0.260428\pi\)
−0.0327533 + 0.999463i \(0.510428\pi\)
\(390\) 5007.61 + 839.362i 0.650180 + 0.108981i
\(391\) −1091.01 1091.01i −0.141112 0.141112i
\(392\) 1720.22 16241.5i 0.221643 2.09265i
\(393\) −5306.93 + 5306.93i −0.681169 + 0.681169i
\(394\) −102.978 + 73.4123i −0.0131675 + 0.00938695i
\(395\) 5370.69 12966.0i 0.684123 1.65162i
\(396\) −3236.99 + 3654.81i −0.410770 + 0.463791i
\(397\) −7615.39 + 3154.40i −0.962734 + 0.398778i −0.808003 0.589179i \(-0.799451\pi\)
−0.154732 + 0.987957i \(0.549451\pi\)
\(398\) 11486.5 2648.63i 1.44665 0.333578i
\(399\) 22234.4i 2.78975i
\(400\) −5670.88 + 690.144i −0.708861 + 0.0862680i
\(401\) 5161.80i 0.642813i −0.946941 0.321407i \(-0.895844\pi\)
0.946941 0.321407i \(-0.104156\pi\)
\(402\) 1839.01 + 7975.34i 0.228163 + 0.989487i
\(403\) 2308.51 956.218i 0.285348 0.118195i
\(404\) 536.642 + 8851.65i 0.0660864 + 1.09007i
\(405\) −3286.76 + 7934.94i −0.403260 + 0.973557i
\(406\) −780.556 1094.92i −0.0954146 0.133842i
\(407\) −2797.46 + 2797.46i −0.340700 + 0.340700i
\(408\) −4614.68 + 1362.91i −0.559953 + 0.165377i
\(409\) 554.377 + 554.377i 0.0670225 + 0.0670225i 0.739823 0.672801i \(-0.234909\pi\)
−0.672801 + 0.739823i \(0.734909\pi\)
\(410\) 1101.61 6572.19i 0.132695 0.791652i
\(411\) −8209.79 3400.61i −0.985302 0.408125i
\(412\) −1785.02 + 5175.08i −0.213450 + 0.618829i
\(413\) 1575.81 + 3804.33i 0.187749 + 0.453266i
\(414\) 4194.68 + 2622.69i 0.497965 + 0.311348i
\(415\) 19676.4 2.32741
\(416\) 1957.83 + 2142.34i 0.230747 + 0.252492i
\(417\) 13460.6 1.58074
\(418\) −4136.95 2586.59i −0.484078 0.302666i
\(419\) 1812.51 + 4375.80i 0.211330 + 0.510195i 0.993628 0.112709i \(-0.0359528\pi\)
−0.782298 + 0.622904i \(0.785953\pi\)
\(420\) −27632.1 9531.02i −3.21026 1.10730i
\(421\) −4077.46 1688.94i −0.472026 0.195520i 0.133973 0.990985i \(-0.457226\pi\)
−0.605999 + 0.795465i \(0.707226\pi\)
\(422\) 840.919 5016.89i 0.0970030 0.578717i
\(423\) −4845.88 4845.88i −0.557008 0.557008i
\(424\) 1011.00 1858.47i 0.115798 0.212866i
\(425\) 1754.63 1754.63i 0.200264 0.200264i
\(426\) −9297.72 13042.3i −1.05746 1.48334i
\(427\) −6428.84 + 15520.6i −0.728602 + 1.75900i
\(428\) 14239.8 863.306i 1.60820 0.0974988i
\(429\) −2194.17 + 908.853i −0.246936 + 0.102284i
\(430\) 599.233 + 2598.73i 0.0672037 + 0.291446i
\(431\) 17343.8i 1.93833i −0.246418 0.969164i \(-0.579254\pi\)
0.246418 0.969164i \(-0.420746\pi\)
\(432\) 1924.45 1086.09i 0.214329 0.120959i
\(433\) 10223.8i 1.13469i −0.823479 0.567347i \(-0.807970\pi\)
0.823479 0.567347i \(-0.192030\pi\)
\(434\) −14016.7 + 3232.06i −1.55028 + 0.357474i
\(435\) −1507.13 + 624.274i −0.166118 + 0.0688084i
\(436\) 11757.8 + 10413.7i 1.29151 + 1.14386i
\(437\) −1891.95 + 4567.56i −0.207103 + 0.499991i
\(438\) −17901.8 + 12762.0i −1.95293 + 1.39222i
\(439\) −12436.5 + 12436.5i −1.35208 + 1.35208i −0.468742 + 0.883335i \(0.655293\pi\)
−0.883335 + 0.468742i \(0.844707\pi\)
\(440\) 4987.87 4032.48i 0.540426 0.436911i
\(441\) −16084.2 16084.2i −1.73676 1.73676i
\(442\) −1243.28 208.395i −0.133793 0.0224261i
\(443\) 9677.23 + 4008.44i 1.03788 + 0.429902i 0.835549 0.549416i \(-0.185150\pi\)
0.202327 + 0.979318i \(0.435150\pi\)
\(444\) 11239.5 5474.44i 1.20136 0.585148i
\(445\) −6400.98 15453.3i −0.681878 1.64620i
\(446\) −3984.92 + 6373.42i −0.423075 + 0.676659i
\(447\) 4939.36 0.522648
\(448\) −9076.90 14026.4i −0.957239 1.47921i
\(449\) −2416.16 −0.253954 −0.126977 0.991906i \(-0.540527\pi\)
−0.126977 + 0.991906i \(0.540527\pi\)
\(450\) −4217.97 + 6746.16i −0.441860 + 0.706704i
\(451\) 1192.82 + 2879.71i 0.124540 + 0.300666i
\(452\) −10014.0 + 4877.53i −1.04208 + 0.507566i
\(453\) 3734.96 + 1547.07i 0.387381 + 0.160458i
\(454\) 6077.63 + 1018.72i 0.628276 + 0.105310i
\(455\) −5414.91 5414.91i −0.557922 0.557922i
\(456\) 9693.23 + 11989.8i 0.995454 + 1.23130i
\(457\) 6285.99 6285.99i 0.643427 0.643427i −0.307969 0.951396i \(-0.599649\pi\)
0.951396 + 0.307969i \(0.0996493\pi\)
\(458\) −13978.1 + 9964.82i −1.42610 + 1.01665i
\(459\) −367.320 + 886.789i −0.0373530 + 0.0901782i
\(460\) −4865.40 4309.18i −0.493153 0.436775i
\(461\) 8841.89 3662.43i 0.893292 0.370014i 0.111655 0.993747i \(-0.464385\pi\)
0.781637 + 0.623733i \(0.214385\pi\)
\(462\) 13322.4 3071.96i 1.34159 0.309352i
\(463\) 7744.43i 0.777353i 0.921374 + 0.388676i \(0.127068\pi\)
−0.921374 + 0.388676i \(0.872932\pi\)
\(464\) −898.248 250.141i −0.0898709 0.0250269i
\(465\) 17450.9i 1.74035i
\(466\) −119.275 517.266i −0.0118568 0.0514204i
\(467\) 7032.30 2912.87i 0.696822 0.288633i −0.00601716 0.999982i \(-0.501915\pi\)
0.702839 + 0.711349i \(0.251915\pi\)
\(468\) 4034.55 244.599i 0.398498 0.0241594i
\(469\) 4723.86 11404.4i 0.465091 1.12283i
\(470\) 5226.31 + 7331.16i 0.512919 + 0.719492i
\(471\) 2638.73 2638.73i 0.258145 0.258145i
\(472\) 2508.27 + 1364.48i 0.244603 + 0.133063i
\(473\) −882.070 882.070i −0.0857455 0.0857455i
\(474\) 3429.21 20458.6i 0.332297 1.98248i
\(475\) −7345.84 3042.75i −0.709580 0.293918i
\(476\) 6860.42 + 2366.34i 0.660603 + 0.227859i
\(477\) −1127.59 2722.24i −0.108236 0.261306i
\(478\) 332.937 + 208.166i 0.0318581 + 0.0199190i
\(479\) −19364.6 −1.84716 −0.923580 0.383405i \(-0.874751\pi\)
−0.923580 + 0.383405i \(0.874751\pi\)
\(480\) −19055.6 + 6906.85i −1.81201 + 0.656777i
\(481\) 3275.34 0.310484
\(482\) 11571.8 + 7235.14i 1.09353 + 0.683717i
\(483\) −5301.61 12799.2i −0.499444 1.20577i
\(484\) 2493.77 7229.88i 0.234201 0.678990i
\(485\) 18923.3 + 7838.27i 1.77167 + 0.733850i
\(486\) −2534.51 + 15120.8i −0.236559 + 1.41130i
\(487\) 2799.10 + 2799.10i 0.260450 + 0.260450i 0.825237 0.564787i \(-0.191042\pi\)
−0.564787 + 0.825237i \(0.691042\pi\)
\(488\) 3299.58 + 11172.1i 0.306076 + 1.03635i
\(489\) 7010.08 7010.08i 0.648276 0.648276i
\(490\) 17346.9 + 24333.2i 1.59929 + 2.24339i
\(491\) −935.299 + 2258.01i −0.0859663 + 0.207541i −0.961016 0.276491i \(-0.910828\pi\)
0.875050 + 0.484032i \(0.160828\pi\)
\(492\) −596.063 9831.78i −0.0546191 0.900917i
\(493\) 374.186 154.993i 0.0341836 0.0141593i
\(494\) 907.599 + 3936.04i 0.0826616 + 0.358484i
\(495\) 8932.98i 0.811126i
\(496\) −6149.38 + 7853.53i −0.556684 + 0.710956i
\(497\) 24157.1i 2.18027i
\(498\) 28339.8 6534.79i 2.55008 0.588014i
\(499\) −552.418 + 228.819i −0.0495583 + 0.0205277i −0.407325 0.913283i \(-0.633538\pi\)
0.357767 + 0.933811i \(0.383538\pi\)
\(500\) −2774.77 + 3132.93i −0.248183 + 0.280218i
\(501\) 2668.89 6443.27i 0.237998 0.574579i
\(502\) −8217.91 + 5858.47i −0.730644 + 0.520869i
\(503\) −254.724 + 254.724i −0.0225797 + 0.0225797i −0.718307 0.695727i \(-0.755082\pi\)
0.695727 + 0.718307i \(0.255082\pi\)
\(504\) −23139.1 2450.77i −2.04503 0.216599i
\(505\) −11473.3 11473.3i −1.01100 1.01100i
\(506\) 2998.19 + 502.548i 0.263410 + 0.0441521i
\(507\) −13710.0 5678.86i −1.20095 0.497450i
\(508\) −3187.30 6543.81i −0.278373 0.571525i
\(509\) −5370.63 12965.8i −0.467680 1.12908i −0.965173 0.261611i \(-0.915746\pi\)
0.497494 0.867468i \(-0.334254\pi\)
\(510\) 4667.45 7465.03i 0.405251 0.648152i
\(511\) 33157.9 2.87049
\(512\) −11009.6 3606.53i −0.950310 0.311304i
\(513\) 3075.60 0.264700
\(514\) 9898.82 15832.0i 0.849452 1.35860i
\(515\) −3833.08 9253.88i −0.327972 0.791796i
\(516\) 1726.15 + 3543.94i 0.147267 + 0.302351i
\(517\) −3890.69 1611.58i −0.330972 0.137093i
\(518\) −18595.9 3116.99i −1.57733 0.264387i
\(519\) 13951.6 + 13951.6i 1.17998 + 1.17998i
\(520\) −5280.63 559.297i −0.445329 0.0471669i
\(521\) 2418.86 2418.86i 0.203402 0.203402i −0.598054 0.801456i \(-0.704059\pi\)
0.801456 + 0.598054i \(0.204059\pi\)
\(522\) −1057.42 + 753.826i −0.0886631 + 0.0632070i
\(523\) −3061.70 + 7391.60i −0.255982 + 0.617996i −0.998665 0.0516471i \(-0.983553\pi\)
0.742683 + 0.669643i \(0.233553\pi\)
\(524\) 5204.11 5875.84i 0.433860 0.489861i
\(525\) 20584.5 8526.38i 1.71120 0.708804i
\(526\) 18756.6 4325.01i 1.55480 0.358516i
\(527\) 4332.65i 0.358128i
\(528\) 5844.79 7464.52i 0.481746 0.615249i
\(529\) 9086.56i 0.746820i
\(530\) 869.787 + 3772.06i 0.0712851 + 0.309147i
\(531\) 3674.06 1521.84i 0.300264 0.124374i
\(532\) −1407.18 23210.8i −0.114678 1.89157i
\(533\) 987.531 2384.11i 0.0802528 0.193747i
\(534\) −14351.6 20131.6i −1.16302 1.63142i
\(535\) −18457.3 + 18457.3i −1.49155 + 1.49155i
\(536\) −2424.51 8209.18i −0.195379 0.661534i
\(537\) 18646.1 + 18646.1i 1.49840 + 1.49840i
\(538\) 481.854 2874.73i 0.0386137 0.230368i
\(539\) −12913.8 5349.06i −1.03198 0.427459i
\(540\) −1318.39 + 3822.25i −0.105064 + 0.304599i
\(541\) 4520.94 + 10914.5i 0.359280 + 0.867379i 0.995402 + 0.0957899i \(0.0305377\pi\)
−0.636121 + 0.771589i \(0.719462\pi\)
\(542\) −322.984 201.943i −0.0255966 0.0160040i
\(543\) −16399.6 −1.29608
\(544\) 4731.07 1714.81i 0.372873 0.135151i
\(545\) −28738.1 −2.25873
\(546\) −9597.45 6000.72i −0.752258 0.470343i
\(547\) 4726.46 + 11410.7i 0.369450 + 0.891930i 0.993841 + 0.110818i \(0.0353471\pi\)
−0.624391 + 0.781112i \(0.714653\pi\)
\(548\) 8785.52 + 3030.35i 0.684852 + 0.236223i
\(549\) 14989.1 + 6208.68i 1.16524 + 0.482660i
\(550\) −808.229 + 4821.87i −0.0626600 + 0.373828i
\(551\) −917.662 917.662i −0.0709505 0.0709505i
\(552\) −8438.78 4590.65i −0.650685 0.353969i
\(553\) −22122.6 + 22122.6i −1.70117 + 1.70117i
\(554\) −843.392 1183.06i −0.0646793 0.0907283i
\(555\) −8753.78 + 21133.5i −0.669509 + 1.61634i
\(556\) −14051.7 + 851.898i −1.07180 + 0.0649793i
\(557\) −2303.67 + 954.213i −0.175242 + 0.0725876i −0.468579 0.883421i \(-0.655234\pi\)
0.293337 + 0.956009i \(0.405234\pi\)
\(558\) 3121.38 + 13536.7i 0.236807 + 1.02698i
\(559\) 1032.75i 0.0781407i
\(560\) 29448.7 + 8200.76i 2.22221 + 0.618831i
\(561\) 4118.04i 0.309918i
\(562\) −22422.4 + 5170.30i −1.68297 + 0.388071i
\(563\) −2533.84 + 1049.55i −0.189677 + 0.0785670i −0.475501 0.879715i \(-0.657733\pi\)
0.285823 + 0.958282i \(0.407733\pi\)
\(564\) 9962.24 + 8823.34i 0.743769 + 0.658740i
\(565\) 7799.30 18829.2i 0.580742 1.40204i
\(566\) −76.3198 + 54.4076i −0.00566778 + 0.00404050i
\(567\) 13538.6 13538.6i 1.00277 1.00277i
\(568\) 10531.4 + 13026.6i 0.777974 + 0.962294i
\(569\) −10461.9 10461.9i −0.770801 0.770801i 0.207445 0.978247i \(-0.433485\pi\)
−0.978247 + 0.207445i \(0.933485\pi\)
\(570\) −27822.2 4663.49i −2.04447 0.342688i
\(571\) 21510.2 + 8909.80i 1.57648 + 0.653001i 0.987852 0.155400i \(-0.0496668\pi\)
0.588632 + 0.808401i \(0.299667\pi\)
\(572\) 2233.00 1087.63i 0.163228 0.0795036i
\(573\) −966.329 2332.92i −0.0704519 0.170086i
\(574\) −7875.59 + 12596.1i −0.572685 + 0.915942i
\(575\) 4954.16 0.359309
\(576\) −13546.1 + 8766.06i −0.979894 + 0.634119i
\(577\) 8321.88 0.600424 0.300212 0.953873i \(-0.402943\pi\)
0.300212 + 0.953873i \(0.402943\pi\)
\(578\) 6208.12 9929.16i 0.446754 0.714531i
\(579\) −2678.21 6465.77i −0.192232 0.464090i
\(580\) 1533.80 747.072i 0.109806 0.0534836i
\(581\) −40524.8 16785.9i −2.89372 1.19862i
\(582\) 29858.3 + 5004.78i 2.12658 + 0.356451i
\(583\) −1280.32 1280.32i −0.0909530 0.0909530i
\(584\) 17880.2 14455.4i 1.26693 1.02426i
\(585\) −5229.48 + 5229.48i −0.369594 + 0.369594i
\(586\) 15165.0 10811.0i 1.06905 0.762114i
\(587\) 7994.94 19301.5i 0.562158 1.35717i −0.345880 0.938279i \(-0.612419\pi\)
0.908037 0.418890i \(-0.137581\pi\)
\(588\) 33066.1 + 29286.0i 2.31909 + 2.05397i
\(589\) −12826.1 + 5312.74i −0.897266 + 0.371660i
\(590\) −5090.94 + 1173.90i −0.355238 + 0.0819132i
\(591\) 342.028i 0.0238057i
\(592\) −11386.6 + 6426.17i −0.790518 + 0.446139i
\(593\) 17757.1i 1.22968i −0.788654 0.614838i \(-0.789222\pi\)
0.788654 0.614838i \(-0.210778\pi\)
\(594\) −424.934 1842.84i −0.0293523 0.127294i
\(595\) −12267.6 + 5081.39i −0.845245 + 0.350112i
\(596\) −5156.26 + 312.604i −0.354377 + 0.0214845i
\(597\) −12200.0 + 29453.5i −0.836371 + 2.01918i
\(598\) −1460.98 2049.37i −0.0999061 0.140142i
\(599\) 17544.2 17544.2i 1.19672 1.19672i 0.221578 0.975143i \(-0.428879\pi\)
0.975143 0.221578i \(-0.0711206\pi\)
\(600\) 7382.97 13571.8i 0.502347 0.923442i
\(601\) 16.0607 + 16.0607i 0.00109006 + 0.00109006i 0.707652 0.706562i \(-0.249755\pi\)
−0.706562 + 0.707652i \(0.749755\pi\)
\(602\) 982.820 5863.48i 0.0665395 0.396972i
\(603\) −11013.9 4562.10i −0.743814 0.308098i
\(604\) −3996.88 1378.63i −0.269256 0.0928734i
\(605\) 5355.04 + 12928.2i 0.359857 + 0.868771i
\(606\) −20335.4 12714.5i −1.36315 0.852298i
\(607\) −15461.8 −1.03390 −0.516950 0.856016i \(-0.672933\pi\)
−0.516950 + 0.856016i \(0.672933\pi\)
\(608\) −10877.7 11902.8i −0.725574 0.793953i
\(609\) 3636.61 0.241975
\(610\) −18072.8 11299.8i −1.19958 0.750028i
\(611\) 1334.22 + 3221.10i 0.0883418 + 0.213276i
\(612\) 2285.30 6625.49i 0.150944 0.437614i
\(613\) 13837.1 + 5731.53i 0.911708 + 0.377642i 0.788710 0.614765i \(-0.210749\pi\)
0.122998 + 0.992407i \(0.460749\pi\)
\(614\) −2780.22 + 16586.7i −0.182737 + 1.09020i
\(615\) 12743.7 + 12743.7i 0.835571 + 0.835571i
\(616\) −13713.0 + 4050.01i −0.896935 + 0.264902i
\(617\) 6349.72 6349.72i 0.414312 0.414312i −0.468926 0.883238i \(-0.655359\pi\)
0.883238 + 0.468926i \(0.155359\pi\)
\(618\) −8594.13 12055.3i −0.559396 0.784688i
\(619\) 7640.34 18445.4i 0.496109 1.19771i −0.455455 0.890259i \(-0.650523\pi\)
0.951563 0.307453i \(-0.0994767\pi\)
\(620\) −1104.44 18217.2i −0.0715408 1.18003i
\(621\) −1770.47 + 733.353i −0.114407 + 0.0473888i
\(622\) 575.264 + 2494.78i 0.0370836 + 0.160823i
\(623\) 37287.9i 2.39793i
\(624\) −7791.44 + 948.215i −0.499851 + 0.0608317i
\(625\) 18815.1i 1.20417i
\(626\) 2229.35 514.059i 0.142337 0.0328210i
\(627\) 12190.8 5049.59i 0.776480 0.321628i
\(628\) −2587.61 + 2921.61i −0.164421 + 0.185645i
\(629\) 2173.37 5246.97i 0.137771 0.332608i
\(630\) 34667.2 24713.9i 2.19234 1.56290i
\(631\) −3471.86 + 3471.86i −0.219037 + 0.219037i −0.808093 0.589055i \(-0.799500\pi\)
0.589055 + 0.808093i \(0.299500\pi\)
\(632\) −2285.01 + 21574.0i −0.143818 + 1.35786i
\(633\) 9727.94 + 9727.94i 0.610823 + 0.610823i
\(634\) 12291.6 + 2060.28i 0.769971 + 0.129060i
\(635\) 12304.2 + 5096.58i 0.768943 + 0.318506i
\(636\) 2505.51 + 5144.03i 0.156210 + 0.320714i
\(637\) 4428.48 + 10691.3i 0.275452 + 0.664999i
\(638\) −423.057 + 676.631i −0.0262523 + 0.0419876i
\(639\) 23329.8 1.44431
\(640\) 19455.3 8416.14i 1.20162 0.519808i
\(641\) 7666.55 0.472403 0.236202 0.971704i \(-0.424097\pi\)
0.236202 + 0.971704i \(0.424097\pi\)
\(642\) −20454.1 + 32714.0i −1.25742 + 2.01109i
\(643\) −3146.10 7595.36i −0.192955 0.465835i 0.797560 0.603240i \(-0.206124\pi\)
−0.990515 + 0.137405i \(0.956124\pi\)
\(644\) 6344.46 + 13025.7i 0.388209 + 0.797028i
\(645\) −6663.62 2760.16i −0.406790 0.168498i
\(646\) 6907.63 + 1157.84i 0.420708 + 0.0705179i
\(647\) −10868.8 10868.8i −0.660428 0.660428i 0.295053 0.955481i \(-0.404663\pi\)
−0.955481 + 0.295053i \(0.904663\pi\)
\(648\) 1398.38 13202.9i 0.0847742 0.800399i
\(649\) 1727.98 1727.98i 0.104513 0.104513i
\(650\) 3295.93 2349.64i 0.198888 0.141785i
\(651\) 14887.4 35941.3i 0.896285 2.16382i
\(652\) −6874.26 + 7761.57i −0.412909 + 0.466206i
\(653\) −2635.05 + 1091.47i −0.157914 + 0.0654099i −0.460240 0.887794i \(-0.652237\pi\)
0.302327 + 0.953204i \(0.402237\pi\)
\(654\) −41391.5 + 9544.33i −2.47483 + 0.570662i
\(655\) 14361.6i 0.856721i
\(656\) 1244.48 + 10225.8i 0.0740680 + 0.608614i
\(657\) 32022.4i 1.90154i
\(658\) −4509.73 19557.6i −0.267185 1.15872i
\(659\) −19323.7 + 8004.13i −1.14225 + 0.473136i −0.871928 0.489633i \(-0.837131\pi\)
−0.270323 + 0.962770i \(0.587131\pi\)
\(660\) 1049.73 + 17314.8i 0.0619102 + 1.02118i
\(661\) 67.1965 162.227i 0.00395407 0.00954598i −0.921890 0.387451i \(-0.873356\pi\)
0.925844 + 0.377905i \(0.123356\pi\)
\(662\) 11176.4 + 15677.6i 0.656168 + 0.920434i
\(663\) 2410.76 2410.76i 0.141216 0.141216i
\(664\) −29170.8 + 8615.34i −1.70489 + 0.503524i
\(665\) 30085.2 + 30085.2i 1.75437 + 1.75437i
\(666\) −3010.25 + 17959.1i −0.175142 + 1.04489i
\(667\) 747.061 + 309.443i 0.0433678 + 0.0179635i
\(668\) −2378.30 + 6895.12i −0.137754 + 0.399372i
\(669\) −7779.43 18781.2i −0.449582 1.08539i
\(670\) 13279.7 + 8303.04i 0.765733 + 0.478768i
\(671\) 9969.74 0.573588
\(672\) 45138.6 + 2031.23i 2.59116 + 0.116602i
\(673\) 3444.70 0.197301 0.0986503 0.995122i \(-0.468547\pi\)
0.0986503 + 0.995122i \(0.468547\pi\)
\(674\) 12114.5 + 7574.45i 0.692331 + 0.432874i
\(675\) −1179.42 2847.38i −0.0672534 0.162364i
\(676\) 14671.4 + 5060.55i 0.834743 + 0.287924i
\(677\) −4665.73 1932.61i −0.264872 0.109714i 0.246295 0.969195i \(-0.420787\pi\)
−0.511167 + 0.859481i \(0.670787\pi\)
\(678\) 4979.90 29709.9i 0.282082 1.68290i
\(679\) −32286.9 32286.9i −1.82483 1.82483i
\(680\) −4399.96 + 8088.24i −0.248133 + 0.456132i
\(681\) −11784.7 + 11784.7i −0.663131 + 0.663131i
\(682\) 4955.37 + 6951.10i 0.278227 + 0.390281i
\(683\) 537.141 1296.77i 0.0300924 0.0726496i −0.908119 0.418712i \(-0.862482\pi\)
0.938211 + 0.346063i \(0.112482\pi\)
\(684\) −22415.9 + 1358.99i −1.25306 + 0.0759683i
\(685\) −15710.0 + 6507.27i −0.876272 + 0.362964i
\(686\) −7855.37 34066.9i −0.437200 1.89603i
\(687\) 46426.1i 2.57826i
\(688\) −2026.24 3590.32i −0.112282 0.198953i
\(689\) 1499.04i 0.0828864i
\(690\) 17127.8 3949.45i 0.944994 0.217903i
\(691\) 10591.5 4387.14i 0.583097 0.241526i −0.0715810 0.997435i \(-0.522804\pi\)
0.654678 + 0.755908i \(0.272804\pi\)
\(692\) −15447.3 13681.3i −0.848580 0.751569i
\(693\) −7620.73 + 18398.1i −0.417731 + 1.00849i
\(694\) 3859.16 2751.16i 0.211083 0.150479i
\(695\) 18213.4 18213.4i 0.994063 0.994063i
\(696\) 1961.02 1585.40i 0.106799 0.0863428i
\(697\) −3163.97 3163.97i −0.171943 0.171943i
\(698\) 21962.1 + 3681.22i 1.19094 + 0.199622i
\(699\) 1326.36 + 549.398i 0.0717706 + 0.0297284i
\(700\) −20948.8 + 10203.6i −1.13113 + 0.550941i
\(701\) 2339.32 + 5647.61i 0.126041 + 0.304290i 0.974286 0.225314i \(-0.0723406\pi\)
−0.848245 + 0.529604i \(0.822341\pi\)
\(702\) −830.058 + 1327.58i −0.0446275 + 0.0713765i
\(703\) −18197.8 −0.976304
\(704\) −5629.03 + 8162.22i −0.301352 + 0.436968i
\(705\) −24349.4 −1.30078
\(706\) −5814.56 + 9299.71i −0.309963 + 0.495750i
\(707\) 13842.2 + 33417.9i 0.736334 + 1.77767i
\(708\) −6942.61 + 3381.54i −0.368530 + 0.179500i
\(709\) 13955.2 + 5780.42i 0.739207 + 0.306189i 0.720329 0.693632i \(-0.243991\pi\)
0.0188776 + 0.999822i \(0.493991\pi\)
\(710\) −30228.1 5066.76i −1.59780 0.267820i
\(711\) 21365.0 + 21365.0i 1.12694 + 1.12694i
\(712\) 16255.9 + 20107.3i 0.855641 + 1.05836i
\(713\) 6116.56 6116.56i 0.321272 0.321272i
\(714\) −15981.4 + 11392.9i −0.837657 + 0.597157i
\(715\) −1739.15 + 4198.68i −0.0909657 + 0.219611i
\(716\) −20645.0 18284.9i −1.07757 0.954381i
\(717\) −981.100 + 406.385i −0.0511016 + 0.0211670i
\(718\) −313.194 + 72.2185i −0.0162790 + 0.00375372i
\(719\) 153.579i 0.00796595i −0.999992 0.00398298i \(-0.998732\pi\)
0.999992 0.00398298i \(-0.00126782\pi\)
\(720\) 7919.93 28440.3i 0.409942 1.47209i
\(721\) 22329.0i 1.15336i
\(722\) −683.578 2964.52i −0.0352357 0.152809i
\(723\) −34099.7 + 14124.6i −1.75406 + 0.726554i
\(724\) 17119.7 1037.90i 0.878798 0.0532781i
\(725\) −497.666 + 1201.47i −0.0254936 + 0.0615469i
\(726\) 12006.5 + 16842.0i 0.613778 + 0.860972i
\(727\) −5550.98 + 5550.98i −0.283184 + 0.283184i −0.834377 0.551194i \(-0.814173\pi\)
0.551194 + 0.834377i \(0.314173\pi\)
\(728\) 10398.7 + 5656.82i 0.529397 + 0.287989i
\(729\) −18117.5 18117.5i −0.920464 0.920464i
\(730\) −6954.62 + 41491.0i −0.352605 + 2.10363i
\(731\) 1654.43 + 685.286i 0.0837088 + 0.0346733i
\(732\) −29783.0 10272.9i −1.50384 0.518713i
\(733\) −827.485 1997.73i −0.0416969 0.100665i 0.901659 0.432448i \(-0.142350\pi\)
−0.943356 + 0.331782i \(0.892350\pi\)
\(734\) −6162.54 3853.08i −0.309896 0.193760i
\(735\) −80819.2 −4.05587
\(736\) 9099.88 + 4258.16i 0.455742 + 0.213258i
\(737\) −7325.69 −0.366140
\(738\) 12164.7 + 7605.90i 0.606762 + 0.379373i
\(739\) −1375.10 3319.78i −0.0684489 0.165250i 0.885953 0.463775i \(-0.153505\pi\)
−0.954402 + 0.298525i \(0.903505\pi\)
\(740\) 7800.68 22615.5i 0.387512 1.12346i
\(741\) −10092.7 4180.54i −0.500358 0.207255i
\(742\) 1426.56 8510.83i 0.0705806 0.421082i
\(743\) 22288.2 + 22288.2i 1.10051 + 1.10051i 0.994349 + 0.106156i \(0.0338544\pi\)
0.106156 + 0.994349i \(0.466146\pi\)
\(744\) −7640.90 25871.4i −0.376517 1.27485i
\(745\) 6683.41 6683.41i 0.328673 0.328673i
\(746\) −14852.8 20834.6i −0.728954 1.02253i
\(747\) −16211.1 + 39137.1i −0.794021 + 1.91694i
\(748\) −260.625 4298.88i −0.0127398 0.210137i
\(749\) 53760.1 22268.2i 2.62263 1.08633i
\(750\) −2543.13 11029.0i −0.123816 0.536961i
\(751\) 24467.3i 1.18885i −0.804151 0.594424i \(-0.797380\pi\)
0.804151 0.594424i \(-0.202620\pi\)
\(752\) −10958.1 8580.30i −0.531385 0.416079i
\(753\) 27294.6i 1.32094i
\(754\) 643.771 148.445i 0.0310939 0.00716983i
\(755\) 7147.08 2960.42i 0.344515 0.142703i
\(756\) 5976.09 6747.47i 0.287498 0.324607i
\(757\) 13698.7 33071.6i 0.657712 1.58786i −0.143616 0.989633i \(-0.545873\pi\)
0.801328 0.598225i \(-0.204127\pi\)
\(758\) 499.151 355.840i 0.0239182 0.0170510i
\(759\) −5813.59 + 5813.59i −0.278024 + 0.278024i
\(760\) 29339.1 + 3107.45i 1.40032 + 0.148315i
\(761\) 23068.9 + 23068.9i 1.09888 + 1.09888i 0.994542 + 0.104338i \(0.0332725\pi\)
0.104338 + 0.994542i \(0.466728\pi\)
\(762\) 19414.4 + 3254.19i 0.922979 + 0.154707i
\(763\) 59188.2 + 24516.5i 2.80833 + 1.16325i
\(764\) 1156.41 + 2374.21i 0.0547611 + 0.112429i
\(765\) 4907.38 + 11847.5i 0.231930 + 0.559929i
\(766\) −6764.75 + 10819.4i −0.319087 + 0.510342i
\(767\) −2023.17 −0.0952441
\(768\) 25226.3 18583.1i 1.18525 0.873126i
\(769\) −22615.1 −1.06050 −0.530249 0.847842i \(-0.677902\pi\)
−0.530249 + 0.847842i \(0.677902\pi\)
\(770\) 13869.8 22183.1i 0.649132 1.03821i
\(771\) 19324.7 + 46653.8i 0.902672 + 2.17924i
\(772\) 3205.03 + 6580.20i 0.149419 + 0.306770i
\(773\) −5061.63 2096.60i −0.235516 0.0975541i 0.261804 0.965121i \(-0.415683\pi\)
−0.497320 + 0.867567i \(0.665683\pi\)
\(774\) −5662.68 949.164i −0.262973 0.0440788i
\(775\) 9837.04 + 9837.04i 0.455944 + 0.455944i
\(776\) −31486.3 3334.87i −1.45656 0.154271i
\(777\) 36058.0 36058.0i 1.66483 1.66483i
\(778\) 12447.4 8873.65i 0.573602 0.408915i
\(779\) −5486.72 + 13246.1i −0.252352 + 0.609231i
\(780\) 9521.79 10750.8i 0.437096 0.493515i
\(781\) 13245.0 5486.24i 0.606840 0.251361i
\(782\) −4252.46 + 980.560i −0.194460 + 0.0448398i
\(783\) 503.039i 0.0229593i
\(784\) −36371.6 28479.3i −1.65687 1.29734i
\(785\) 7140.90i 0.324675i
\(786\) 4769.67 + 20684.9i 0.216449 + 0.938686i
\(787\) −4514.92 + 1870.14i −0.204497 + 0.0847056i −0.482581 0.875851i \(-0.660301\pi\)
0.278084 + 0.960557i \(0.410301\pi\)
\(788\) 21.6464 + 357.048i 0.000978581 + 0.0161412i
\(789\) −19921.7 + 48095.2i −0.898899 + 2.17013i
\(790\) −23042.3 32322.4i −1.03773 1.45567i
\(791\) −32126.4 + 32126.4i −1.44410 + 1.44410i
\(792\) 3911.32 + 13243.4i 0.175483 + 0.594171i
\(793\) −5836.41 5836.41i −0.261358 0.261358i
\(794\) −3854.11 + 22993.5i −0.172264 + 1.02772i
\(795\) −9672.24 4006.37i −0.431496 0.178731i
\(796\) 10871.7 31519.0i 0.484092 1.40347i
\(797\) −3175.58 7666.53i −0.141135 0.340731i 0.837468 0.546486i \(-0.184035\pi\)
−0.978603 + 0.205755i \(0.934035\pi\)
\(798\) 53323.4 + 33340.0i 2.36545 + 1.47898i
\(799\) 6045.40 0.267673
\(800\) −6848.24 + 14635.0i −0.302652 + 0.646782i
\(801\) 36011.0 1.58850
\(802\) −12379.2 7740.01i −0.545045 0.340785i
\(803\) −7530.40 18180.0i −0.330936 0.798951i
\(804\) 21884.4 + 7548.47i 0.959952 + 0.331112i
\(805\) −24492.1 10145.0i −1.07234 0.444178i
\(806\) 1168.33 6970.20i 0.0510578 0.304609i
\(807\) 5574.19 + 5574.19i 0.243149 + 0.243149i
\(808\) 22033.1 + 11985.9i 0.959309 + 0.521858i
\(809\) −24242.4 + 24242.4i −1.05355 + 1.05355i −0.0550636 + 0.998483i \(0.517536\pi\)
−0.998483 + 0.0550636i \(0.982464\pi\)
\(810\) 14101.5 + 19780.7i 0.611698 + 0.858054i
\(811\) 8971.75 21659.7i 0.388460 0.937825i −0.601807 0.798642i \(-0.705552\pi\)
0.990267 0.139183i \(-0.0444477\pi\)
\(812\) −3796.30 + 230.155i −0.164069 + 0.00994688i
\(813\) 951.771 394.236i 0.0410579 0.0170067i
\(814\) 2514.25 + 10903.7i 0.108261 + 0.469503i
\(815\) 18970.6i 0.815351i
\(816\) −3651.04 + 13110.8i −0.156632 + 0.562462i
\(817\) 5737.95i 0.245711i
\(818\) 2160.81 498.254i 0.0923605 0.0212971i
\(819\) 15231.7 6309.19i 0.649866 0.269183i
\(820\) −14109.9 12496.8i −0.600899 0.532204i
\(821\) −13914.2 + 33592.0i −0.591486 + 1.42797i 0.290580 + 0.956851i \(0.406152\pi\)
−0.882067 + 0.471124i \(0.843848\pi\)
\(822\) −20465.9 + 14589.9i −0.868406 + 0.619078i
\(823\) −16528.3 + 16528.3i −0.700050 + 0.700050i −0.964421 0.264371i \(-0.914836\pi\)
0.264371 + 0.964421i \(0.414836\pi\)
\(824\) 9734.49 + 12040.8i 0.411550 + 0.509056i
\(825\) −9349.78 9349.78i −0.394567 0.394567i
\(826\) 11486.6 + 1925.35i 0.483862 + 0.0811036i
\(827\) −42195.4 17477.9i −1.77422 0.734905i −0.993998 0.109399i \(-0.965107\pi\)
−0.780219 0.625506i \(-0.784893\pi\)
\(828\) 12579.7 6127.20i 0.527988 0.257168i
\(829\) 10495.1 + 25337.5i 0.439699 + 1.06153i 0.976053 + 0.217535i \(0.0698015\pi\)
−0.536353 + 0.843994i \(0.680198\pi\)
\(830\) 29504.3 47188.7i 1.23387 1.97342i
\(831\) 3929.37 0.164029
\(832\) 8073.57 1482.96i 0.336419 0.0617938i
\(833\) 20065.6 0.834611
\(834\) 20183.8 32281.7i 0.838021 1.34032i
\(835\) −5107.09 12329.6i −0.211662 0.510998i
\(836\) −12406.5 + 6042.86i −0.513264 + 0.249996i
\(837\) −4971.63 2059.31i −0.205310 0.0850422i
\(838\) 13212.0 + 2214.57i 0.544633 + 0.0912899i
\(839\) −24243.8 24243.8i −0.997605 0.997605i 0.00239210 0.999997i \(-0.499239\pi\)
−0.999997 + 0.00239210i \(0.999239\pi\)
\(840\) −64291.4 + 51976.9i −2.64079 + 2.13497i
\(841\) 17095.5 17095.5i 0.700953 0.700953i
\(842\) −10164.5 + 7246.20i −0.416025 + 0.296580i
\(843\) 23815.2 57495.0i 0.973000 2.34903i
\(844\) −10770.8 9539.45i −0.439272 0.389054i
\(845\) −26234.9 + 10866.9i −1.06806 + 0.442404i
\(846\) −18887.9 + 4355.29i −0.767587 + 0.176995i
\(847\) 31194.9i 1.26549i
\(848\) −2941.09 5211.35i −0.119101 0.211036i
\(849\) 253.485i 0.0102469i
\(850\) −1577.00 6839.07i −0.0636360 0.275974i
\(851\) 10475.5 4339.11i 0.421971 0.174786i
\(852\) −45220.3 + 2741.53i −1.81834 + 0.110239i
\(853\) −2422.60 + 5848.66i −0.0972428 + 0.234765i −0.965014 0.262200i \(-0.915552\pi\)
0.867771 + 0.496965i \(0.165552\pi\)
\(854\) 27582.2 + 38690.7i 1.10520 + 1.55031i
\(855\) 29054.9 29054.9i 1.16217 1.16217i
\(856\) 19281.9 35445.1i 0.769910 1.41529i
\(857\) 9164.60 + 9164.60i 0.365294 + 0.365294i 0.865758 0.500464i \(-0.166837\pi\)
−0.500464 + 0.865758i \(0.666837\pi\)
\(858\) −1110.46 + 6624.95i −0.0441846 + 0.263604i
\(859\) −35659.4 14770.6i −1.41639 0.586689i −0.462442 0.886650i \(-0.653027\pi\)
−0.953952 + 0.299960i \(0.903027\pi\)
\(860\) 7130.92 + 2459.64i 0.282747 + 0.0975267i
\(861\) −15374.9 37118.2i −0.608565 1.46921i
\(862\) −41594.5 26006.6i −1.64352 1.02760i
\(863\) −2066.31 −0.0815043 −0.0407521 0.999169i \(-0.512975\pi\)
−0.0407521 + 0.999169i \(0.512975\pi\)
\(864\) 280.972 6243.85i 0.0110635 0.245857i
\(865\) 37755.7 1.48409
\(866\) −24519.0 15330.3i −0.962114 0.601553i
\(867\) 12119.6 + 29259.3i 0.474744 + 1.14613i
\(868\) −13266.4 + 38461.7i −0.518770 + 1.50401i
\(869\) 17153.7 + 7105.29i 0.669619 + 0.277365i
\(870\) −762.751 + 4550.55i −0.0297238 + 0.177331i
\(871\) 4288.55 + 4288.55i 0.166834 + 0.166834i
\(872\) 42605.1 12583.1i 1.65458 0.488665i
\(873\) −31181.3 + 31181.3i −1.20885 + 1.20885i
\(874\) 8117.19 + 11386.3i 0.314151 + 0.440672i
\(875\) −6532.55 + 15771.0i −0.252389 + 0.609321i
\(876\) 3763.02 + 62069.2i 0.145138 + 2.39398i
\(877\) −218.985 + 90.7068i −0.00843172 + 0.00349253i −0.386895 0.922124i \(-0.626453\pi\)
0.378464 + 0.925616i \(0.376453\pi\)
\(878\) 11177.5 + 48474.0i 0.429637 + 1.86323i
\(879\) 50368.5i 1.93275i
\(880\) −2191.66 18008.7i −0.0839554 0.689858i
\(881\) 6300.18i 0.240929i 0.992718 + 0.120464i \(0.0384384\pi\)
−0.992718 + 0.120464i \(0.961562\pi\)
\(882\) −62691.6 + 14455.9i −2.39335 + 0.551875i
\(883\) −16904.8 + 7002.21i −0.644272 + 0.266866i −0.680803 0.732466i \(-0.738369\pi\)
0.0365310 + 0.999333i \(0.488369\pi\)
\(884\) −2364.05 + 2669.19i −0.0899451 + 0.101555i
\(885\) 5407.18 13054.1i 0.205379 0.495829i
\(886\) 24124.0 17197.8i 0.914742 0.652111i
\(887\) 8766.03 8766.03i 0.331832 0.331832i −0.521450 0.853282i \(-0.674609\pi\)
0.853282 + 0.521450i \(0.174609\pi\)
\(888\) 3724.38 35163.9i 0.140745 1.32885i
\(889\) −20993.5 20993.5i −0.792013 0.792013i
\(890\) −46659.0 7820.85i −1.75732 0.294557i
\(891\) −10497.7 4348.31i −0.394711 0.163495i
\(892\) 9309.68 + 19113.6i 0.349452 + 0.717456i
\(893\) −7412.93 17896.4i −0.277787 0.670638i
\(894\) 7406.46 11845.8i 0.277080 0.443156i
\(895\) 50459.9 1.88457
\(896\) −47249.3 + 736.322i −1.76170 + 0.0274540i
\(897\) 6806.70 0.253366
\(898\) −3622.97 + 5794.52i −0.134633 + 0.215329i
\(899\) 868.941 + 2097.81i 0.0322367 + 0.0778263i
\(900\) 9854.15 + 20231.4i 0.364969 + 0.749313i
\(901\) 2401.40 + 994.692i 0.0887927 + 0.0367791i
\(902\) 8694.86 + 1457.41i 0.320961 + 0.0537987i
\(903\) 11369.5 + 11369.5i 0.418995 + 0.418995i
\(904\) −3318.29 + 31329.7i −0.122085 + 1.15267i
\(905\) −22190.2 + 22190.2i −0.815056 + 0.815056i
\(906\) 9310.74 6637.53i 0.341422 0.243396i
\(907\) −10784.4 + 26035.9i −0.394808 + 0.953150i 0.594069 + 0.804414i \(0.297521\pi\)
−0.988877 + 0.148736i \(0.952479\pi\)
\(908\) 11556.4 13048.1i 0.422371 0.476890i
\(909\) 32273.5 13368.1i 1.17761 0.487781i
\(910\) −21105.8 + 4866.72i −0.768846 + 0.177286i
\(911\) 39106.7i 1.42224i 0.703070 + 0.711121i \(0.251812\pi\)
−0.703070 + 0.711121i \(0.748188\pi\)
\(912\) 43289.2 5268.28i 1.57176 0.191283i
\(913\) 26031.4i 0.943606i
\(914\) −5649.61 24501.0i −0.204456 0.886676i
\(915\) 53256.9 22059.7i 1.92417 0.797019i
\(916\) 2938.24 + 48464.8i 0.105985 + 1.74817i
\(917\) 12251.9 29578.6i 0.441213 1.06518i
\(918\) 1575.95 + 2210.64i 0.0566601 + 0.0794794i
\(919\) 22104.3 22104.3i 0.793422 0.793422i −0.188626 0.982049i \(-0.560404\pi\)
0.982049 + 0.188626i \(0.0604035\pi\)
\(920\) −17630.0 + 5206.88i −0.631788 + 0.186593i
\(921\) −32162.2 32162.2i −1.15068 1.15068i
\(922\) 4474.83 26696.7i 0.159838 0.953590i
\(923\) −10965.5 4542.05i −0.391043 0.161975i
\(924\) 12609.3 36556.6i 0.448935 1.30154i
\(925\) 6978.44 + 16847.4i 0.248054 + 0.598854i
\(926\) 18573.0 + 11612.6i 0.659122 + 0.412110i
\(927\) 21564.4 0.764042
\(928\) −1946.80 + 1779.13i −0.0688652 + 0.0629342i
\(929\) −48663.4 −1.71862 −0.859308 0.511459i \(-0.829105\pi\)
−0.859308 + 0.511459i \(0.829105\pi\)
\(930\) 41851.4 + 26167.2i 1.47566 + 0.922641i
\(931\) −24604.6 59400.8i −0.866147 2.09106i
\(932\) −1419.38 489.580i −0.0498855 0.0172068i
\(933\) −6397.08 2649.76i −0.224470 0.0929787i
\(934\) 3559.01 21232.9i 0.124683 0.743858i
\(935\) 5572.10 + 5572.10i 0.194895 + 0.194895i
\(936\) 5463.11 10042.6i 0.190777 0.350697i
\(937\) 16318.9 16318.9i 0.568960 0.568960i −0.362877 0.931837i \(-0.618205\pi\)
0.931837 + 0.362877i \(0.118205\pi\)
\(938\) −20267.2 28429.6i −0.705488 0.989617i
\(939\) −2367.83 + 5716.46i −0.0822911 + 0.198668i
\(940\) 25418.6 1541.03i 0.881984 0.0534713i
\(941\) 16638.7 6891.96i 0.576414 0.238758i −0.0753798 0.997155i \(-0.524017\pi\)
0.651793 + 0.758397i \(0.274017\pi\)
\(942\) −2371.59 10285.0i −0.0820283 0.355737i
\(943\) 8933.39i 0.308495i
\(944\) 7033.46 3969.42i 0.242500 0.136858i
\(945\) 16491.9i 0.567707i
\(946\) −3438.06 + 792.771i −0.118162 + 0.0272465i
\(947\) −22740.2 + 9419.31i −0.780315 + 0.323217i −0.737043 0.675846i \(-0.763778\pi\)
−0.0432725 + 0.999063i \(0.513778\pi\)
\(948\) −43922.6 38901.3i −1.50479 1.33276i
\(949\) −6234.40 + 15051.2i −0.213253 + 0.514839i
\(950\) −18312.2 + 13054.6i −0.625396 + 0.445838i
\(951\) −23833.8 + 23833.8i −0.812687 + 0.812687i
\(952\) 15962.1 12904.7i 0.543419 0.439331i
\(953\) 36291.7 + 36291.7i 1.23358 + 1.23358i 0.962578 + 0.271005i \(0.0873560\pi\)
0.271005 + 0.962578i \(0.412644\pi\)
\(954\) −8219.38 1377.71i −0.278944 0.0467558i
\(955\) −4464.20 1849.13i −0.151265 0.0626560i
\(956\) 998.463 486.323i 0.0337789 0.0164527i
\(957\) −825.900 1993.90i −0.0278971 0.0673496i
\(958\) −29036.8 + 46440.9i −0.979264 + 1.56622i
\(959\) 37907.1 1.27642
\(960\) −12009.2 + 56056.6i −0.403744 + 1.88460i
\(961\) −5500.75 −0.184645
\(962\) 4911.30 7855.05i 0.164602 0.263261i
\(963\) −21505.6 51919.1i −0.719635 1.73735i
\(964\) 34703.3 16903.0i 1.15946 0.564738i
\(965\) −12372.7 5124.92i −0.412736 0.170961i
\(966\) −38645.3 6477.62i −1.28715 0.215749i
\(967\) −7129.16 7129.16i −0.237082 0.237082i 0.578559 0.815641i \(-0.303615\pi\)
−0.815641 + 0.578559i \(0.803615\pi\)
\(968\) −13599.6 16821.7i −0.451559 0.558544i
\(969\) −13394.1 + 13394.1i −0.444047 + 0.444047i
\(970\) 47173.1 33629.2i 1.56148 1.11316i
\(971\) 3934.25 9498.11i 0.130027 0.313912i −0.845436 0.534077i \(-0.820659\pi\)
0.975463 + 0.220164i \(0.0706594\pi\)
\(972\) 32462.9 + 28751.7i 1.07124 + 0.948776i
\(973\) −53049.7 + 21973.9i −1.74789 + 0.723999i
\(974\) 10910.1 2515.73i 0.358914 0.0827609i
\(975\) 10947.0i 0.359573i
\(976\) 31741.0 + 8839.12i 1.04099 + 0.289891i
\(977\) 16541.9i 0.541682i −0.962624 0.270841i \(-0.912698\pi\)
0.962624 0.270841i \(-0.0873018\pi\)
\(978\) −6300.40 27323.3i −0.205996 0.893358i
\(979\) 20444.4 8468.35i 0.667422 0.276455i
\(980\) 84368.2 5114.92i 2.75004 0.166725i
\(981\) 23677.0 57161.3i 0.770589 1.86037i
\(982\) 4012.80 + 5628.91i 0.130401 + 0.182918i
\(983\) 20577.7 20577.7i 0.667678 0.667678i −0.289500 0.957178i \(-0.593489\pi\)
0.957178 + 0.289500i \(0.0934891\pi\)
\(984\) −24472.8 13313.1i −0.792849 0.431305i
\(985\) −462.796 462.796i −0.0149705 0.0149705i
\(986\) 189.374 1129.80i 0.00611652 0.0364910i
\(987\) 50149.3 + 20772.5i 1.61729 + 0.669905i
\(988\) 10800.5 + 3725.37i 0.347783 + 0.119959i
\(989\) 1368.17 + 3303.05i 0.0439891 + 0.106199i
\(990\) −21423.4 13394.8i −0.687759 0.430015i
\(991\) −31319.0 −1.00392 −0.501958 0.864892i \(-0.667387\pi\)
−0.501958 + 0.864892i \(0.667387\pi\)
\(992\) 9613.79 + 26523.9i 0.307700 + 0.848926i
\(993\) −52070.9 −1.66407
\(994\) 57934.5 + 36223.0i 1.84866 + 1.15586i
\(995\) 23345.5 + 56361.1i 0.743822 + 1.79574i
\(996\) 26823.0 77764.6i 0.853333 2.47396i
\(997\) −12142.4 5029.56i −0.385712 0.159767i 0.181397 0.983410i \(-0.441938\pi\)
−0.567109 + 0.823643i \(0.691938\pi\)
\(998\) −279.576 + 1667.94i −0.00886755 + 0.0529035i
\(999\) −4987.78 4987.78i −0.157964 0.157964i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 32.4.g.a.5.8 44
4.3 odd 2 128.4.g.a.113.2 44
8.3 odd 2 256.4.g.a.225.10 44
8.5 even 2 256.4.g.b.225.2 44
32.3 odd 8 256.4.g.a.33.10 44
32.13 even 8 inner 32.4.g.a.13.8 yes 44
32.19 odd 8 128.4.g.a.17.2 44
32.29 even 8 256.4.g.b.33.2 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.g.a.5.8 44 1.1 even 1 trivial
32.4.g.a.13.8 yes 44 32.13 even 8 inner
128.4.g.a.17.2 44 32.19 odd 8
128.4.g.a.113.2 44 4.3 odd 2
256.4.g.a.33.10 44 32.3 odd 8
256.4.g.a.225.10 44 8.3 odd 2
256.4.g.b.33.2 44 32.29 even 8
256.4.g.b.225.2 44 8.5 even 2